Looking at a creek on a Sunday stroll, and seeing lots and lots of concepts from hydrodynamics class.

For example below, you see waves radiating from each of the ducks. And you see interference of waves from all those ducks.

What happens if the ducks bring their waves closer?

At some point, all those waves from the ducks are going to hit the weir in the picture below.

And there, they are going to somehow react to the flow field caused by the changes in topography.

And you can spot so many different phenomena: Standing waves, hydraulic jumps, and lots more!

Watch the movie below to see the whole thing even better!

Btw, you might remember this spot, I have talked about standing waves from right there before. Interestingly, the wave pattern in the other post looks really different, probably due to different water levels or changes in topography (maybe someone threw in rocks or they did some construction work on the weir?). But it is still just as fascinating as last time :-)

This is a method that I have been excited about ever since learning about #birdclass in the “Evidence-based undergraduate STEM teaching” MOOC last year: Help students discover that the content of your class is not restricted to your class, but actually occurs everywhere! All the time! In their own lives!

The idea is that students take pictures or describe their observations related to course materials in short messages, which are posted somewhere so every participant of the class can see them.

One example where I would use this: Hydraulic jumps. As I said on Tuesday, hydraulic jumps are often taught in a way that students have a hard time realizing that they can actually observe them all the time. Most students have observed the phenomenon, maybe even consciously, yet are not able to put it together with the theory they hear about during their lectures. So why not, in your class on hydrodynamics, ask students to send in pictures of all the hydraulic jumps they happen to see in their everyday life? The collection that soon builds will likely look something like the image below: Lots of sinks, some shots of people hosing their decks or cars, lots of rivers. But does it matter if students send in the 15th picture of a sink? No, because they still looked at the sink, recognized that what they saw was a hydraulic jump, and took a picture. Even if all of this only takes 30 seconds, that’s probably 30 extra seconds a student thought about your content, that otherwise he or she would have only thought about doing their dishes or cleaning their deck or their car.

A collection of images, all showing hydraulic jumps of some kind.

And even if you do this with hydraulic jumps, and not with Taylor columns or whatever comes next in your class, once students start looking at the world through the kind of glasses that let them spot the hydraulic jumps, they are also going to look at waves on a puddle and tell you whether those are shallow water or deep water waves, and they are going to see refraction of waves around pylons. In short: They have learned to actually observe the kind of content you care about in class, but in their own world.

The “classic” method uses twitter to share pictures and observations, which apparently works very well. And of course you can either make it voluntary or compulsory to send in pictures, or give bonus points, and specify what kind and quality of text should come with the picture.

You, as the instructor, can also use the pictures in class as examples. Actually, I would recommend picking one or two occasionally and discussing for a minute or two why they are great examples and what is interesting about them. You can do this as introduction to that day’s topic or as a random anecdote to engage students. But acknowledging the students’ pictures and expanding on their thoughts is really useful to keep them engaged in the topic and make them excited to submit more and better pictures (hence to find better examples in their lives, which means to think more about your course’s topic!).

And you don’t even have to use twitter. Whatever learning management system you might be using might work, too, and there are many other platforms. I recently gave a workshop for instructors at TU Dresden and talked about how awesome it would be if they made their students take pictures of everything related to their class. They were (legitimately!) a bit reluctant at first, because you cannot actually see the topic of the course, measuring and automation technology (MAT), just the fridge or camera or whatever gadget that uses MAT. But still, going about your everyday life thinking about which of the technical instruments around you might be using MAT, and discovering that most of them do, is pretty awesome, isn’t it? And documenting those thoughts might already be a step towards thinking more about MAT. At least that is what I claimed, and it seems to have worked out pretty well.

We are about to try this for a course on ceramics (and I imagine we’ll see tons of false teeth, maybe some knees, some fuses, many sinks and coffee cups and flower pots, maybe the occasional piece of jewelry ), and I am hoping they will relate what they take pictures of to processes explained in class (like sintering, which seems to be THE process in that class ;-))

I am going to try to implement it in other courses, too. Because this is one of the most important motivators, isn’t it? The recognition that what that one person talks about in front of the class all the time is actually occurring in – and relevant to – my own life. How awesome is that? :-)

Hydraulic jumps, especially submerged ones, are a very theoretical concept for many students, one that occurs in a lab experiment if they are lucky, but more likely only seems to exists in videos, drawings, and text books. But we can observe them all the time if we know what we are looking for! They don’t only occur in hard-to-see places like the Denmark Strait (for you oceanographers) or inside some big plant, mixing in one chemical or another (for you engineers), they are everywhere!

So. Submerged hydraulic jumps. You don’t think about them for years and years, then one day a friend (Hi, Sindre!) asks about them and the next day you come across this:

A tiny waterfall in Schleswig

A tiny waterfall that not only shows a beautiful submerged hydraulic jump, but provides extra entertainment in the form of two empty bottles caught up in the return flow above the submerged hydraulic jump:

Litter caught up in the return flow above a submerged hydraulic jump

You should watch the video, it is really entertaining!

So what is going on here? Below a sketch: Water from the reservoir (A) flows down over a sill. It actually doesn’t flow, but it shoots (B), meaning that it flows faster than waves can propagate. Any wave in the flow that would normally propagate in all directions now cannot propagate upstream any more and is just flushed downstream. At (C), the flow has slowed down enough again that wave speed is the same as flow speed, we are at the hydraulic jump. In this case it is submerged – meaning that it occurs below the water’s surface. We can also think of non-submerged hydraulic jumps – see for example here. But what also happens with submerged hydraulic jumps is that the water jet shooting down the slope is so fast that it entrains water from outside the jet and pulls it down with it. This water has to come from somewhere, so we get a return flow (D). And this is exactly where the bottles are caught: In the flow that goes back towards the jet shooting down the slope.

When the bottles come too close to the jet, they get pulled under water and then “jump” because they are too buoyant to actually sink. They might jump away a little from the jet, but as you see in the movie, the return flow reaches out quite a bit from where the jet enters the water, trapping the bottles.

This is actually what makes man-made waterfalls so dangerous: You saw in the movie that the return flow pattern is very similar over the whole width of the “waterfall”. So anything trapped in there will have a really hard time getting out. If either the sill or the slope were a little more irregular, it might break up the symmetry and allow things (and animals or people) to get out more easily. Of course, in this case the drop isn’t very high, but imagine a larger weir. Not fun to get caught in the return flow there!

Talking to my Norwegian friends about these things and especially using movies from my reality to illustrate concepts always makes me want to apologize for how tiny our waterfalls are, how in the middle of a city everything is, how much litter there is everywhere, how regulated even the tiniest streams around here are. But then I realize that it is actually really cool that even in the middle of the city we can spot all this. You don’t need the wide open, pristine nature to get yourself – and your students! – excited about oceanographic phenomena!

The most impressive hydraulic jump might be in the Denmark Strait, but there are others around, too! [deutscher Text unten]

When filling the big wave tank with a hose, we can see a hydraulic jump. Of course, the flow field isn’t mainly controlled by hydraulics, but still we see the Froude number changing from greater 1 to less than 1 – there is a clear boundary where the surface height jumps up and waves, that were flushed away closer to the point of impact, start propagating.

The standing waves are caused by rocks sitting in a current. From the pictures below it is not really clear where those rocks are situated, whether they are upstream of all this wave action or in the focal point of the wave fronts.

More standing waves.

Having stood there with my mom for quite some time the other weekend, just watching the water, I can tell you that it’s the upstream obstacle. You can see for yourself here:

What you also see in that video is that not all of the waves are, in fact, standing waves. The lower-amplitude waves to the left on both the image above and below are not – they are radiating away from some obstacle.

More standing waves.

Just from looking at that image it is clear that the bathymetry is very irregular and that the current speed is quite inhomogeneous, too. So maybe it is not surprising that the condition for a standing wave – that the current speed and the wave speed are the same, but going in opposite directions – is not met everywhere. Particularly, in many cases it is hypercritical and the waves are just flushed away. Note the current speed in the video below.

And all of this action is happening on an exciting river called … wait for it … Pinnau. In Mölln. And this is what it looks like to most people: Tiny little rapids somewhere in a forest.

P.S.: I just realized that when I’ve talked about standing waves before on this blog, I’ve always talked about the see-sawing kind. When obviously this kind is so much cooler!

Recently in Bergen, I was walking to meet up with a friend at the kayak club, and I had to cross a bridge that has always fascinated me. Underneath the bridge, there is only a very narrow opening connecting basically the ocean on one side and a small bay on the other side. On this part of the Norwegian coast, the tidal range is easily of the order of a meter, so this narrow opening under the bridge makes for some pretty strong currents. In fact, when paddling through that opening, when the tide is right you can really see how the surface elevation changes from one side of the bridge to the other.

So when I was walking there recently, this is what I saw:

Strong current from the lower left to the upper right of the picture, wind blowing from the right, hence waves on the right side of the current and no waves on the left side.

This might be difficult to see on this picture, but there is a strong current going from the lower left corner of the picture towards the upper right. And on the right side of that current there are a lot of wind waves. But on the left side there are hardly any, even though there is nothing blocking the wind, just the current blocking the propagation of waves. Wind is coming from the right here.

I found it really fascinating how this current acted as a barrier to the waves and stood a couple of minutes watching. A couple of people stopped and looked, too, but didn’t find anything interesting to see and were slightly puzzled. But what I see is fetch (or that there isn’t enough of it on the left side of the current) and hydraulic jumps (or that the current is clearly going faster than the waves are). Which means that I start wondering how fast that current would have to be in order to stop waves from propagating across. Which then means I start estimating the wave lengths in oder to estimate the waves’ velocities to answer the previous question. So that’s reason enough to stand there for quite some time, just watching, right?

I am really fascinated by the hydraulic jumps in my kitchen sink. I can’t believe I haven’t used this before when I was teaching! Yes, movies of rivers and rapids are always really impressive, too, but how cool is it to be able to observe hydraulic jumps in your own sink? Let me remind you:

So this is what happens when the water jet hits the (more or less) level bottom of the sink. But what would happen if it instead hit a slope?

Now, if I wasn’t working a full-time job, or if that job wasn’t completely unrelated to anything to do with hydraulic jumps, I would now proudly present movies of all kinds of hydraulic jumps on sloped surfaces. As it is, I can tell you that I have tons of ideas of where to go to make really nice movies, but for now this is all I can offer:

Yes, that is a chopping board in a sink. It shows really nicely how the hydraulic jump occurs closer to the point of impact of the jet as you go uphill (because the water slows down faster going in that direction than going downhill) and again how the radius depends on the flow speed of the jet. Stay tuned for a more elaborate post on this!

Water changing its velocity from above to below the critical velocity.

Recently in beautiful Wetzlar: The river Lahn flows through the city below the medieval cathedral at sunset. And I’m showing you this because we can observe a hydraulic jump!

A hydraulic jump occurs when water that was flowing faster than the critical speed suddenly slows down to below the critical speed. Some of its kinetic energy is converted to potential energy (see the higher surface levels of the turbulent part of the fluid {except in this example the water is flowing down a steep slope, so the higher levels are a bit tricky to observe}) and a lot of energy is lost to turbulence. A very nice example can be seen here:

As the water moves away from where the jet hits the sink, it slows down. Can you spot the hydraulic jump? Isn’t it cool to watch how it is pushed away if the flow rate is higher, and how it comes back again when the tap is slowly closed?

P.S.: Yes, I’m being very vague about what that critical speed might be. Stay tuned for a post on that, I’m working on it! Just had to share the Lahn movie :-)